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1) A talk radio station has four telephone lines. If the host is unable to talk (i.e., during a commercial) or is talking to a parson, the other callers arc place on hold. When all lines are in use, others who are trying to call in get a busy signal. The probability that 0,1,2,3, or 4 people will get through is shown in the distribution. Find the variance and standard deviation for the distribution.
|
x
|
0
|
1
|
2
|
3
|
4
|
|
P(x)
|
0.18
|
0.34
|
0.23
|
0.21
|
0.04
|
2) The statistical bulletin published by Metropolitan Life Insurance Co. reported that 2% of all American births result in twins. If a random sample of 800 births is taken, find the mean, variance, and standard deviation of the number of births that would result in twins. Please interpret your results.
3) A survey found that one out of five Americans say he or she has visited a doctor in any given month. If 10 people are selected at random. find the probability that exactly three will have visited a doctor last month.
4) A survey found that women spend on average $14621 on beauty products during the summer months. Assume the standard deviation is 329.44. Find the percentage of women who spend less than 3160.00. Assume the variable is normally distributed. Interpret the results.
5) To quality for a policy academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume the test scores are normally distributed.